Photonic band gap (PBG) materials are those periodic composites that possess spectral gaps in the frequency spectrum, in which electromagnetic waves cannot propagate in any direction within the material. Conventional photonic band gap materials are based on Bragg scattering. The Bragg scattering mechanism imposes several constraints on the realization of PBG and its application because it requires periodicity and long range order, and the overall dimension of the PBG crystal must be at least a few times the wavelength at the spectral gap. This latter limitation in particular makes such conventional PBG materials unsuitable for use at, for example, radio frequencies because the material sample would have to be very large for the dimensions to be comparable with the wavelength of the radiation. Such limitations make these PBG structures too bulky and difficult to fabricate for lower frequency applications.
Another bandgap material that can be artificially constructed is based on so-called local resonances. Resonances can also create classical wave band gaps. For example, the interaction of EM waves with the electron gas in metals (plasmon) and the optical phonons in ionic crystals (polariton) can create spectral gaps in which EM waves cannot propagate.
In the field of mathematics, fractal patterns have proven to be useful tools in the analysis of mathematically complex and chaotic patterns. They have yet, however, to find widespread practical applications in physical sciences. Fractal patterns may be applied in the field of antennas as follows, for example: a microstrip patch antenna formed with a fractal structure on at least one surface of a substrate; or an antenna structure with a fractal ground counterpoise and a fractal antenna structure. It is also possible to tune fractal antennas and fractal resonators.
Also, metallic fractal configurations on a dielectric plate can be used for generating multiple stop and pass bands, while its inverse pattern can have the reverse characteristics. Such planar resonating structures employing two-dimensional periodically arranged arrays of metallic elements may be etched on dielectric plates. They are frequently used as filtering devices, denoted frequency selective surfaces (FSS) in the engineering community. For the fractal plate, there are a multitude of internal resonances. The fractal plate behaves like a system with negative dielectric constant in the vicinities of resonance frequencies, and thus possesses a series of spectral gaps for the incident wave.